rport updates, new logo, app.r logic updated, 4pl XL made nicer

dev/Doc_BioassayLinReport.Rmd

@@ -6,13 +6,15 @@ output:
     toc: true
     toc_depth: 3
 header_includes:
-  -\usepackage{fancyheadr}
   -\setlength{\headheight}{22pt}%
-  -\usepackage{lastpage}
-  -\pagestyle{fancy}
   -\usepackage{pdflscape}
   -\usepackage{longtable}
-  -\rhead{\includegraphics[width=.15\textwidth]{`r getwd()`/logo.png}}
+  -\usepackage{fancyheadr}
+  -\pagestyle{fancy}
+  -\fancyhf{}
+  -\fancyfoot[C]{Page \thepage \ of \pageref{LastPage}}
+  -\usepackage{lastpage}
+  -\rhead{\includegraphics[width=.15\textwidth]{`r getwd()`/logov2.png}}
 params:
   FileName: NA
   newTitle: NA
@@ -24,7 +26,7 @@ params:
   Assay: NA
 author: "Author: `r params$author`"
 title: |
-    | ![](logo.png){width=1in}
+    | ![](logov2.png){width=1in}
     | Linear bioassay evaluation
 subtitle: |
   `r params$FileName`
@@ -34,10 +36,7 @@ date: "`r paste(params$NoP, params$Assay)`"
 
 ---
 
-<!-- \fancyfoot[C]{\thepage\ of \pageref{LastPage}} -->
-<!-- \newpage -->
 
-<!-- \newpage -->
 
 ```{r setup, include=FALSE}
 
@@ -69,6 +68,8 @@ ANOVAlin <- LinTests[,4:ncol(LinTests)]
 ```
 
 
+\newpage
+
 # Introduction
 
 Bioassay potency estimation uses statistical methods to quantify the strength of a biological product or drug by comparing its response to that of a reference standard. Biological responses are inherently variable, affected by assay conditions, cell systems or organisms, and measurement noise. To control this variability, a linear regression approach is used to obtain reliable potency values. Three consecutive dilution steps showing the steepest slope are used for linear fitting.   
@@ -139,7 +140,7 @@ plot_grid(XLplotLin)
 ```
 
 
-The relative potency can be read from tbale 3.
+The relative potency can be read from tabale 3.
 
 ```{r LinPotTab, echo=FALSE, warning=FALSE, results='asis'}
 
@@ -148,7 +149,9 @@ kable(LinPotTab, format = "markdown", caption= "Potency table", digits=3)
 
 ```
 
-
+  0 ... test passed;
+  
+  1 ... test failed);
 
 
 The ANOVA of the unconstrained model is listed in table 4.
@@ -173,7 +176,6 @@ kable(LinTests1, row.names = F, format = "markdown", caption="Assay suitability
 
 ```
 
-
 The estimate is the p-value of the test.  
 F-tests on regression, significance of slopes, and preparation need to have a p-value <0.05 to pass.
 All other tests pass if p-value > 0.05.
@@ -209,6 +211,22 @@ kable(SuModABu, format = "markdown", caption= "Restricted linear regression (SSS
 
 SSSI: separate slope, separate intercept
 
+# Signature
+
+<!-- Signature and date:\\ -->
+<!-- \noindent\framebox(200,50) -->
+<!--   \begin{minipage}[t][40pt][c]{190pt} -->
+<!--     \centering -->
+<!--     % Leave this blank for a physical signature -->
+<!--   \end{minipage} -->
+
+
+\vspace{1.5cm} 
+\noindent
+\begin{tabular}{p{6cm}p{1cm}p{6cm}}
+  \cline{1-1} \cline{3-3}
+  Date & & Signature 
+\end{tabular}
 
 
 
@@ -216,12 +234,22 @@ SSSI: separate slope, separate intercept
 
 ## Potency of linear PLA
 
+Relative potency of the test sample to the reference is calculated as:
 $$
- rel Potency = \frac{I_{ref} - I_{test}}{k}
+ relPot_{log} = \frac{I_{ref} - I_{test}}{k}
 $$
-where: I... intercept of reference or test
+where: \\ I... intercept of reference or test\\
 k ... common slope
 
+The standard error of the linear restricted model is used to get the confidence interval of the relative potency with the formula:
+$$
+ CI_{rel Pot} = exp(relPot_{log} \pm se(relPot_{log})*q^{t_{n-p}}_{1-\frac{\alpha}{2}})
+$$
+In general, the confidence intervals are calculated as follows:
+$$
+ CI = \hat\theta\pm se(\hat\theta)*q^{t_{n-p}}_{1-\frac{\alpha}{2}}
+$$
+…where $\hat\theta$ is a fitted parameter or a linear combination thereof, q is the 1-alpha/2 quantile of the Student’s t-distribution with n-p degrees of freedom and se is the standard error derived from any covariance matrix.
 
 
 # Literature